The radius
is smaller when the TRM element size \(\rho _0\)  is smaller (we have \(\partial R/\partial \rho _0 >0\) ) and when the random medium is more scattering
(we have \(\partial R / \partial D<0\) ).
It is not surprising that time-reversal refocusing is improved when the TRM has many array elements and better resolve
the wave field on the mirror, moreover,
it is well-known that random scattering improves time-reversal refocusing by multipathing [1]}, [2]}.
When \(\rho _0\)  becomes very small, i.e. smaller than \(c_o L /(\omega _0 r_0)\) 
and \(c_o / (\omega _0 DL)\) , then the radius of the refocused wave
is equal to
\(R=\frac{\sqrt{2} c_o L }{\omega _0 \sqrt{ r_0^2 +\frac{DL^3}{12} } } ,\) 
